The present invention generally relates to a method to measure the physical characteristics of crystals, and, in particular, to a method and apparatus which simultaneously measures the diffraction resolution and mosaic spread of macromolecular crystals.
The use of reflective mosaicity has been used since 1981 (Shaikevitch et al., 1981) as an indicator of macro-molecular crystal perfection. Subsequently, synchrotron radiation was used to minimize the geometric and spectral contributions of the X-ray source to the experimental data (Colapietro et al., 1992; Helliwell, 1988). Mosaicity analysis of chicken egg-white lysozyme, apocrustacyanin C1 and thaumatin crystals established a physical basis for the improvements seen in some microgravity-grown samples. In these samples, a reduction in the mosaic spread produced a corresponding increase in the signal-to-noise ratio of the reflection (Ng et al., 1997; Snell et al., 1995, 1997). The minimum mosaicities recorded were 0.005xc2x0 for lysozyme, 0.030xc2x0 for apocrustacyanin C1, and 0.018xc2x0 for thaumatin measured at the full-width at half-maximum (FWHM). These values were obtained by deconvoluting the spectral and geometric contributions of the X-ray beam from the recorded rocking width, which allowed a quantitative comparison between samples (Colapietro et al., 1992) independent of the instrument measuring them.
Successful measurement of mosaicity requires that the geometric and spectral parameters of the instrumentation do not mask the crystal characteristics. Synchrotron radiation is a useful tool for these studies, as it can provide a highly parallel and (when a suitable monochromator is used) a highly monochromatic beam (Helliwell, 1992; Margaritondo 1995). Specially configured in house x-ray sources could also be used.
Previous efforts have been devoted to reflections recorded individually with a scintillation counter mounted in the equatorial (vertical) plane by rotating the crystal about the horizontal axis which minimized the Lorentz effect and eliminated the contribution from the horizontal beam divergence of the synchrotron beam (Colapietro et al., 1992; Fourme et al., 1995; Helliwell, 1998; Ng et al. 1997; Snell et al., 1995). An algorithm and software for mosaic spread analysis using data from an area detector was developed in 1998 (Ferrer et al., 1998).
There is still a need for a method to accurately measure the physical characteristics of crystals where the measuring instrument itself does not mask the measurements being made.
There is a particular need for a method to simultaneously measure the diffraction resolution, mosaicity, and intensity data of macromolecular crystals.
The present invention addresses these needs. Typical measurements of macromolecular crystal mosaicity are dominated by the characteristics of the X-ray beam and, as a result, the mosaicity value given during data processing can be an artifact of the instrumentation rather than the sample. The present invention is an improved method for mosaic spread analysis which uses superfine "PHgr"-slicing data collection, unfocused monochromatic radiation, and a suitable fast readout area detector, such as a charge-coupled device (CCD) X-ray area detector.
According to the invention, a fast readout area detector is used to rapidly record many reflections simultaneously. Suitable available protein crystallography software is used to assign indices which identify each reflection and to obtain standard crystallographic statistics, such as l/"sgr"(l) and diffraction resolution. Because the data are not all on the equatorial plane, horizontal divergence is a contributor to the recorded rocking width in addition to the vertical divergence and spectral spread contributions present in other methods. These effects are deconvoluted from the data so that the true crystal mosaicity is evaluated. The fast readout area detector makes the superfine "PHgr"-slicing technique efficient and practical. The development of the crystal-quality evaluation method and the deconvolution of the beam divergence, spectral divergence and Lorentz effects from the measured rocking widths of the reflections are described herein. It is to be understood that the crystal rotations used in super fine "PHgr" slicing can range from less than about 0.0001xc2x0 to greater than about 1xc2x0, and that all such measurements are within the scope of the present invention. The processing is also described, along with examples of the technique using single crystals of manganese superoxide dismutase (MnSOD), insulin and lysozyme.
The present invention provides a method to physically characterize crystals by simultaneously measuring the diffraction resolution and mosaic spread of macromolecular crystals. The contributions of the X-ray beam to the reflection angular widths are minimized by using a highly parallel, highly monochromatic X-ray source. Many, tens to thousands, of reflection profiles over a wide resolution range are rapidly measured using an area detector (e.g. charge-coupled device (CCD)) in combination with superfine "PHgr"-slice data collection. The Lorentz effect and beam contributions are evaluated and deconvoluted from the recorded data. For example, from 1xc2x0 of superfine "PHgr"-slice data collected on a crystal of manganese superoxide dismutase, the mosaicities of 260 reflections were measured. The average mosaicity was 0.0101xc2x0 (s.d. 0.0035xc2x0) measured as the full-width at half-maximum (FWHM) and range from 0.0011 to 0.0188xc2x0. Each reflection profile was individually fitted with two Gaussian profiles, with the first Gaussian contributing 55% (s.d. 9%) and the second contributing 35% (s.d. 9%) of the reflection. On average, the deconvoluted width of the first Gaussian was 0.0054xc2x0 (s.d. 0.0015xc2x0) and the second was 0.0061xc2x0 (s.d. 0.0023xc2x0). The mosaicity of the crystal was anisotropic, with FWHM values of 0.0068, 0.0140xc2x0 and 0.0046xc2x0 along the a, b and c axes, respectively. The anisotropic mosaicity analysis indicates that the crystal is most perfect in the direction that corresponds to the favored growth direction of the crystal.
Methods according to this aspect of the present invention can be used, for example, to inspect a crystal""s structure and its perfection. This method is of particular benefit in studying practical techniques of sample preparation for structural crystallography and for the use of crystals as a device rather than merely as a step to a structural solution.
In particular, the present invention relates to a method to simultaneously measure diffraction resolution and mosaic spread of a macromolecular crystal including the steps of (a) minimizing contributions of an x-ray beam to any reflection angular widths in the crystal by using a highly parallel, highly monochromatic x-ray source; (b) rapidly measuring multiple reflection profiles in the crystal over a wide resolution range using a suitable fast readout area detector in combination with superfine oscillation "PHgr"-slicing imaging data collection; and (c) evaluating and deconvoluting the Lorenz effect and beam contributions from the recorded data.
In certain aspects, the method further includes the step of: (d) determining the direction in which the crystal is most imperfect.
In still further aspects, the method further includes the step of: (e) measuring accurate intensities through file slicing, deconvolution and profile fitting.
The superfine oscillating "PHgr" slice data can be collected on a crystal where from about 0.0001xc2x0 to about 1xc2x0 of the super fine oscillation data is collected and where multiple reflection profiles are measured as the full-width at half-maximum (FWHM) or as the full width at quarter maximum (FWQM). Each reflection profile is fitted with at least one mathematical function that fits the recorded data. Preferably, the mathematical function is at least one Gaussian profile, is at least one Lorentzian profile, or other mathematical function.
Also the fast readout area detector is composed of a charge coupled device(s).
Mosaicity is determined from the measured reflection widths using formula   η  =                              "LeftBracketingBar"                      ϕ            R                    "RightBracketingBar"                -                              (                                          L                2                            ⁢                              xe2x80x83                            ⁢                              ζ                2                            ⁢                              xe2x80x83                            ⁢                              γ                v                2                                      )                                1            2                                                (                      L            /            d                    )                ⁢                  xe2x80x83                ⁢        cos        ⁢                  xe2x80x83                ⁢                  θ          hkl                      ⁢          xe2x80x83        ⁢          (                        δ          ⁢                      xe2x80x83                    ⁢          λ                λ            )        ⁢          xe2x80x83        ⁢    tan    ⁢          xe2x80x83        ⁢                  θ        hkl            .      
In a preferred aspect, the diffraction data are processed by (a) indexing and integrating the 1xc2x0 oscillation images using MOSFLM and scaling of data with suitable software to provide statistics on crystal quality, including the agreement between symmetry-related reflections Rsym and the signal-to-noise ratio l/"sgr"(l); (b) using an orientation matrix to integrate the coarse oscillation image that corresponds with the superfine "PHgr"-sliced images; (c) obtaining a reflection profile from the crystal by integrating the super fine "PHgr"-sliced data; (d) removing random radiation events from the diffraction data; (e) locating the "PHgr" position of the maximum value of the reflection; (f) calculating the width of the reflection as full width half-minimum (FWHM) and full-width at quarter-miminum (FWQM) and true crystal mosaicity xcex7; and (g) fitting one or more mathematical functions that fit the data to all the reflection profiles.
In a preferred aspect, the accurate positioning of the maximum of the reflection allows for the increased accuracy in orientation matrix resulting in more accurate cell parameters.
Step (g) preferably comprises fitting the at least one mathematical function to the reflection profile wherein lmax/lbkg is greater than some arbitrary value (e.g. lmax/lbkg greater than 1-10). The mathematical function preferably is at least one Guassian profile or at least one Lorentzian profile. Also a suitable signal-to-noise ratio can be used to filter out noise.
The reflection list includes indices for each reflection along with its detector coordinates for each reflection along with its detector coordinates for each reflection and the estimated error for each reflection. In a preferred aspect, 0.001xc2x0 images are integrated at the reflection coordinate positions for reflections with a desired signal-to-noise ratio.
Further, in step (g) two Gaussian functions can be used. The initial Guassians are placed as follows before a fitting algorithm is employed. One Guassian function is placed at the maximum and the second Gaussian function is placed at the FWQM value to the right or left of the maximum by comparing the ratio of FWHM to FMQM for each side with that of a perfect Guassian.
The quality of the crystal is quantitatively analyzed by examining the reflection profiles recorded near a vertical equatorial axis. The relative contributions of domain misalignment and volume are distinguished from a variation of d spacing within a domain by analyzing mosaicity as a function of resolution. Then, angular separation between multiple peaks are used to measure misalignment of discrete domains. Thereafter, an anisotropic xcex7 calculation is applied to each individual mathematical function that were fit to the data profiles and then the measured mosaicity is used to identify types of imperfections existing with the crystal.
In another aspect, the present invention relates to a method for comparing different samples of crystals using symmetry related reflections obtained by using the methods described above.
In the methods described above, the Gaussian profile (s) is fit to the recorded data and deconvoluted using   η  =                              "LeftBracketingBar"                      ϕ            R                    "RightBracketingBar"                -                              (                                          L                2                            ⁢                              xe2x80x83                            ⁢                              ζ                2                            ⁢                              xe2x80x83                            ⁢                              γ                v                2                                      )                                1            2                                                (                      L            /            d                    )                ⁢                  xe2x80x83                ⁢        cos        ⁢                  xe2x80x83                ⁢                  θ          hkl                      ⁢          xe2x80x83        ⁢          (                        δ          ⁢                      xe2x80x83                    ⁢          λ                λ            )        ⁢          xe2x80x83        ⁢    tan    ⁢          xe2x80x83        ⁢                  θ        hkl            .      
Further, a Fourier deconvolution can be used to remove inaccuracies in any broad reflection, and then the mathematical functions are fit to the data profile. The formula F({overscore (xcfx89)})=G({overscore (xcfx89)})/I({overscore (xcfx89)}) can be applied where F({overscore (xcfx89)}),G({overscore (xcfx89)}), and I({overscore (xcfx89)}) are the Fourier transforms of the true sample profile, the measured profile and the instrument function, respectively.